Mathematics
In the adjoining figure, AB and CD are equal chords. AD and BC intersects at E. Prove that AE = CE and BE = DE.
Circles
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Answer
In △AEB and △CED,
∠A = ∠C (∵ angles in same segment of a circle are equal.)
∠B = ∠D (∵ angles in same segment of a circle are equal.)
AB = CD (Given)
∴ △AEB ≅ △CED (By ASA axiom)
As corresponding part of congruent triangles are congruent hence,
AE = CE and BE = DE.
Hence, proved that AE = CE and BE = DE.
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